波浪通過潛堤高階諧和波生成現象探討

Harmonic Generation of Water Waves Propagating over An Impermeable Submerged Trapezoidal Obstacle

王超弘(Chao-Hong Wang)

指導教授 ： 丁肇隆

共同指導教授 ： 楊智傑

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.02689

摘要

本文採用實驗方式與數值方法探討單一週期波通過梯形潛堤所產生之複雜波場。利用流場可視化並搭配接圖技巧，在不考慮碎波條件下，研究波浪通過潛堤時，因非線性效應增強導致波浪產生變形，並產生高階諧和波之現象。將兩者方法分析結果，作一定性與定量上的比較，其中結果包含時序列、空間序列波形、堤前與堤上反射率和全域波浪總能之分析，以確保數值模式模擬之效果良好。此外，本文也利用數值方法模擬波浪通過潛堤之方式，探討高階諧和波生成之現象，討論潛堤堤寬與堤上水深對生成強弱之影響。
　　從結果發現，數值計算之波速較實驗為快，波高亦較實驗稍大，然而在堤上非線性效應較強的區域，卻觀察到實驗波速大於數值的現象。數值反射率較實驗大，且都有振幅越小反射率越大的情形，不過差異不大。從平均總能結果可發現，兩者皆有入射波振幅越大，諧和波生成越明顯的現象，且數值之諧和波生成現象較實驗強烈，出堤後兩者也發現主頻波與倍頻波之間有能量互相傳遞的現象。
　　本文同時利用數值方法探討諧和波生成的現象，從結果看出，堤寬對諧和波生成的影響不明顯。相反的，水深呈現而越淺諧和波生成越多的現象，並發現入射條件之Ur數(Ur=(aL^2)/h^3 )與諧和波生成的振幅比例呈現線性的關係。

關鍵字

流場可視化 ； 潛堤 ； 高階諧和波 ； 反射率 ； 波浪總能 ； Ur數

並列摘要

Monochromatic surface waves propagating over a impermeable submerged trapezoidal breakwater under non-breaking conditions were investigated in this research experimentally and numerically. The effect of nonlinearity due to waves shoaling will induce wave deformations as well as the generations of super harmonics. A flow visualization measurement system and image-connection technique were used to record wave profiles, such that surface wave profiles could be analyzed.Numerical calculations were verified by experiment data. Based on the measured results, wave profiles, the reflection coefficients and wave energy were calculated in this research.
From the comparisons of numerical results and experimental data, it shows that the wave celerity and the wave height of numerical results are faster and larger than those from experimental measurements. However, above the breakwaters, the measured wave celerity was faster than the velocity from numerical calculation. It was also observed that the larger the incident wave amplitude, the more apparent super harmonics were generated. After wave transmitting over the breakwaters, waves entered to deep water and wave-wave interaction were observed during propagation.
To study the mechanism of harmonic generation, different widths of and water depths above breakwaters were examined numerically. It was found the widths have no apparent effects on the generation of harmonic. However harmonics are generated more easily in shallow water than in deep water. A parameter was proposed to describe the mechanism of harmonic generation successfully.

並列關鍵字

Flow Visualization ； submerged breakwater ； harmonic generation ； wave reflection coefficients ； wave energy ； Ursell number

參考文獻

28.許展豪，2006。「波浪通過不透水潛堤之流場實驗研究」，國立台灣大學工程科學暨海洋工程學系碩士班論文。

32.王如君，2012。「二波共存之質量與能量傳輸」，國立台灣大學工程科學暨海洋工程學系碩士班論文。

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